On the integral operators pertaining to a family of incomplete <i>I</i>-functions

Abstract

This paper introduces a new incomplete <i>I</i>-functions. The incomplete <i>I</i>-function is an extension of the <i>I</i>-function given by Saxena ^{[<span class="xref"><a href="#b1" ref-type="bibr">1</a></span>]} which is a extension of a familiar Fox's <i>H</i>-function. Next, we find the several interesting classical integral transform of these functions and also find the some basic properties of incomplete <i>I</i>-function. Further, numerous special cases are obtained from our main results among which some are explicitly indicated. Incomplete special functions thus obtained consisting of probability theory has many potential applications which are also presented. Finally, we find the solution of non-homogeneous heat conduction equation in terms of Incomplete <i>I</i>-function.